Burridge-Knopoff Models as Elastic Excitable Media

We construct a model of an excitable medium with elastic rather than the usual diffusive coupling. We explore the dynamics of elastic excitable media, which we find to be dominated by low dimensional structures, including global oscillations, period-doubled pacemakers, and propagating fronts. We suggest that examples of elastic excitable media are to be found in such diverse physical systems as Burridge-Knopoff models of frictional sliding, electronic transmission lines, and active optical waveguides

Active biopolymer networks generate scale-free but euclidean clusters

We report analytical and numerical modelling of active elastic networks, motivated by experiments on crosslinked actin networks contracted by myosin motors. Within a broad range of parameters, the motor-driven collapse of active elastic networks leads to a critical state. We show that this state is qualitatively different from that of the random percolation model. Intriguingly, it possesses both euclidean and scale-free structure with Fisher exponent smaller than $2$. Remarkably, an indistinguishable Fisher exponent and the same euclidean structure is obtained at the critical point of the random percolation model after absorbing all enclaves into their surrounding clusters. We propose that in the experiment the enclaves are absorbed due to steric interactions of network elements. We model the network collapse, taking into account the steric interactions. The model shows how the system robustly drives itself towards the critical point of the random percolation model with absorbed enclaves, in agreement with the experiment.Comment: 6 pages, 7 figure

Dense active matter model of motion patterns in confluent cell monolayers

Epithelial cell monolayers show remarkable displacement and velocity correlations over distances of ten or more cell sizes that are reminiscent of supercooled liquids and active nematics. We show that many observed features can be described within the framework of dense active matter, and argue that persistent uncoordinated cell motility coupled to the collective elastic modes of the cell sheet is sufficient to produce swirl-like correlations. We obtain this result using both continuum active linear elasticity and a normal modes formalism, and validate analytical predictions with numerical simulations of two agent-based cell models, soft elastic particles and the self-propelled Voronoi model together with in-vitro experiments of confluent corneal epithelial cell sheets. Simulations and normal mode analysis perfectly match when tissue-level reorganisation occurs on times longer than the persistence time of cell motility. Our analytical model quantitatively matches measured velocity correlation functions over more than a decade with a single fitting parameter.Comment: updated version accepted for publication in Nat. Com

Instabilities and Oscillations in Isotropic Active Gels

We present a generic formulation of the continuum elasticity of an isotropic crosslinked active gel. The gel is described by a two-component model consisting of an elastic network coupled frictionally to a permeating fluid. Activity is induced by active crosslinkers that undergo an ATP-activated cycle and transmit forces to the network. The on/off dynamics of the active crosslinkers is described via rate equations for unbound and bound motors. For large activity motors yield a contractile instability of the network. At smaller values of activity, the on/off motor dynamics provides an effective inertial drag on the network that opposes elastic restoring forces, resulting in spontaneous oscillations. Our work provides a continuum formulation that unifies earlier microscopic models of oscillations in muscle sarcomeres and a generic framework for the description of the large scale properties of isotropic active solids.Comment: 13 pages, 5 figure

Activity driven fluctuations in living cells

We propose a model for the dynamics of a probe embedded in a living cell, where both thermal fluctuations and nonequilibrium activity coexist. The model is based on a confining harmonic potential describing the elastic cytoskeletal matrix, which undergoes random active hops as a result of the nonequilibrium rearrangements within the cell. We describe the probe's statistics and we bring forth quantities affected by the nonequilibrium activity. We find an excellent agreement between the predictions of our model and experimental results for tracers inside living cells. Finally, we exploit our model to arrive at quantitative predictions for the parameters characterizing nonequilibrium activity, such as the typical time scale of the activity and the amplitude of the active fluctuations.Comment: 6 pages, 4 figure

Incompressible limit of mechanical model of tumor growth with viscosity

Various models of tumor growth are available in the litterature. A first class describes the evolution of the cell number density when considered as a continuous visco-elastic material with growth. A second class, describes the tumor as a set and rules for the free boundary are given related to the classical Hele-Shaw model of fluid dynamics. Following the lines of previous papers where the material is described by a purely elastic material, or when active cell motion is included, we make the link between the two levels of description considering the 'stiff pressure law' limit. Even though viscosity is a regularizing effect, new mathematical difficulties arise in the visco-elastic case because estimates on the pressure field are weaker and do not imply immediately compactness. For instance, traveling wave solutions and numerical simulations show that the pressure may be discontinous in space which is not the case for the elastic case.Comment: 17 page

Non-linear modeling of active biohybrid materials

Recent advances in engineered muscle tissue attached to a synthetic substrate motivates the development of appropriate constitutive and numerical models. Applications of active materials can be expanded by using robust, non-mammalian muscle cells, such as those of Manduca sexta. In this study, we propose a model to assist in the analysis of biohybrid constructs by generalizing a recently proposed constitutive law for Manduca muscle tissue. The continuum model accounts (i) for the stimulation of muscle fibers by introducing multiple stress-free reference configurations for the active and passive states and (ii) for the hysteretic response by specifying a pseudo-elastic energy function. A simple example representing uniaxial loading-unloading is used to validate and verify the characteristics of the model. Then, based on experimental data of muscular thin films, a more complex case shows the qualitative potential of Manduca muscle tissue in active biohybrid constructs

Multi-channel pulse dynamics in a stabilized Ginzburg-Landau system

We study the stability and interactions of chirped solitary pulses in a system of nonlinearly coupled cubic Ginzburg-Landau (CGL) equations with a group-velocity mismatch between them, where each CGL equation is stabilized by linearly coupling it to an additional linear dissipative equation. In the context of nonlinear fiber optics, the model describes transmission and collisions of pulses at different wavelengths in a dual-core fiber, in which the active core is furnished with bandwidth-limited gain, while the other, passive (lossy) one is necessary for stabilization of the solitary pulses. Complete and incomplete collisions of pulses in two channels in the cases of anomalous and normal dispersion in the active core are analyzed by means of perturbation theory and direct numerical simulations. It is demonstrated that the model may readily support fully stable pulses whose collisions are quasi-elastic, provided that the group-velocity difference between the two channels exceeds a critical value. In the case of quasi-elastic collisions, the temporal shift of pulses, predicted by the analytical approach, is in semi-quantitative agrement with direct numerical results in the case of anomalous dispersion (in the opposite case, the perturbation theory does not apply). We also consider a simultaneous collision between pulses in three channels, concluding that this collision remains quasi-elastic, and the pulses remain completely stable. Thus, the model may be a starting point for the design of a stabilized wavelength-division-multiplexed (WDM) transmission system.Comment: a text file in the revtex4 format, and 16 pdf files with figures. Physical Review E, in pres